hân tích các đa thức sau thành nhân tử a) x^2-y^2-2x+2y b) 2x+2y-x^2-xy c) 3a^2- 6ab +3b^2- 12c^2 d) x^2-25+y^2+2xy e) a^2+2ab+b- ac- bc g) x^2- 2x -4

0 bình luận về “hân tích các đa thức sau thành nhân tử a) x^2-y^2-2x+2y b) 2x+2y-x^2-xy c) 3a^2- 6ab +3b^2- 12c^2 d) x^2-25+y^2+2xy e) a^2+2ab+b- ac- bc g) x^2- 2x -4”

1. `a. x^2-y^2-2x+2y`

   $=\left(x^2-y^2\right)-\left(2x-2y\right)$

   $=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)$

   $=\left(x-y\right)\left(x+y-2\right)$

   `b. 2x+2y-x^2-xy`

    `=2(x+y)-x(x+y)`

   `=(x+y)(2-x)`

   `c. 3a^2-6ab+3b^2-12c^2`

   $=3\left(a^2-2ab+b^2-4c^2\right)$

   $=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]$

   $=4\left(a-b-2c\right)\left(a-b+2c\right)$

   `d. x^2-25+y^2+2xy`

   $=\left(x^2+2xy+y^2\right)-25$

   $=\left(x+y\right)^2-5^2$

   $=\left(x+y-5\right)\left(x+y+5\right)$

   `e. a^2 + 2ab + b^2 – ac – bc`

   `=(a^2 + 2ab + b^2) – (ac + bc)`

   `=(a+b)^2- c(a+b)`

   `=(a+b)(a+b-c)`

   `g. x^2- 2x -4y^2- 4y`

   `=(x-2y)(x+2y)-2(x+2y)`

   `=(x+2y)(x-2y-2)`

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2. a/ \(x^2-y^2-2x+2y\\=(x^2-y^2)-(2x-2y)\\=(x-y)(x+y)-2(x-y)\\=(x-y)(x+y-2)\)

   b/ \( 2x+2y-x^2-xy\\=(2x+2y)-(x^2+xy)\\=2(x+y)-x(x+y)\\=(2-x)(x+y)\)

   c/ \( 3a^2-6ab+3b^2-12c^2\\=3(a^2-2ab+b^2-4c^2)\\=3[(a^2-2ab+b)^2-(2c)^2]\\=3[(a-b)^2-(2c)^2]\\=3(a-b-2c)(a-b+2c)\)

   d/ \(x^2-25+y^2+2xy\\=(x^2+2xy+y^2)-5^2\\=(x+y)^2-5^2\\=(x+y-5)(x+y+5)\)

   e/ \(a^2+2ab+b^2-ac-bc\\=(a^2+2ab+b^2)-(ac+bc)\\=(a+b)^2-c(a+b)\\=(a+b)(a+b-c)\)

   g/ \(x^2-2x-4y^2-4y\\=(x^2-4y^2)-(2x+4y)\\=(x-2y)(x+2y)-2(x+2y)\\=(x+2y)(x-2y-2)\)

    

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